? re: ordinal logistic regression, non-linear predictor variables

Question

Hello,

I'm trying to figure out if I can use the ordinal logistic regression function with the data I have in order to create a set of prediction equations for estimating age-at-death.  My response variables are ordinal (adolescent, young adult, middle adult, old adult), and my four predictor variables are continuous, but two are non-linear.  I've tried transforming the predictor variables, but I can't seem to find a linear solution. If I've read correctly, the ordinal logistic regression analysis in JMP is based on a general linear model, so would that negate my being able to use the function due to my non-linear response variables (determined by the means of these variables when graphed by age category - i.e., the mean values rise to an asymptote in middle adulthood, then fall in value in old adulthood)?  I've tried performing the analysis using the non-linear platform, but I receive an cautionary message because my Y variable is not continuous.

*Any* constructive advice is much appreciated!  Also, on the most basic level, am I understanding the assumptions of the logistic model correctly?

Many thanks,

Kate

reeza · Answer

The assumptions for the independent variables isn't linearity ( and I don't even know what that would mean?)

A generalized linear models means the model is a linear combination, but the terms themselves can be quadratic.  A non-linear model may have order statistics (max/min) and/or division/multiplication of terms that can't be expressed in a linear fashion.

y=x+ x^2 is still a GLM

y=cx/ax is a nonlinear model.

mohammadfayaz · Answer

Hi,

In linear regression models, the response variable is continues.

In logistic regression models, the response variable is dichotomous. So we we choose appropriate link function ( probit,logit) to model it.

In all of the GLM models, the predictor variables can be continuous and discrete ( nominal, ordinal).

I don't understand (but two are non-linear):

"My response variables are ordinal (adolescent, young adult, middle adult, old adult), and my four predictor variables are continuous, but two are non-linear."

Your response variable is ordinal. So you can break it to 4 logistic regression:

* If it is "adolescent" code 1 , other code 0 -> with only this dichotomous response and all other predictor variables , model a logistic regression.
* If it is "young adult" code 1 , other code 0 -> with only this dichotomous response and all other predictor variables , model a logistic regression.
* If it is "middle adult" code 1 , other code 0 -> with only this dichotomous response and all other predictor variables , model a logistic regression.
* If it is "middle adult" code 1 , other code 0 -> with only this dichotomous response and all other predictor variables , model a logistic regression.

You can also fit ordinal logistic regression, as you mentioned. Check this example in JMP website.

For more statistical details about these models , read "Introduction to categorical data analysis" or "categorical data analysis" by Alan Agresti , Wiley.